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Number Theory: Unique Numbers

  1. May 17, 2014 #1
    Does anyone know of a reference work that lists natural numbers with unique properties? Like 26, for example, being the only natural number sandwiched between a square (25) and a cube (27). Does such a reference book exist?

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  3. May 17, 2014 #2


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  4. May 17, 2014 #3
    Thanx Micro, I was aware of certain Wikipedia articles; what I specifically am looking for though, is a systematic reference work of all know unique numbers. I could not find something resembling this on the net...
  5. May 17, 2014 #4


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    It depends a lot on the things you consider as unique properties. Every number has unique properties, but most of them are boring ("is the only number x where x-23 and x-24 are primes" is another one for 26). Random collections are the best things you can find.
  6. May 17, 2014 #5
    Hmm...is that a trivial uniqueness quality that you just mentioned for 26? Doesn't seem so to me but then I am the layman here...

    Can one somehow 'define' mathematical triviality for such unique qualities I wonder...

  7. May 17, 2014 #6


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    It is trivial in the way that "x-23 prime and x-24 prime" requires two primes with a difference of just 1, and 2 and 3 are the only primes that satisfy this.
    You can set this up for every integer.
  8. May 17, 2014 #7
    Yes, if course...silly me...
  9. May 18, 2014 #8


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  10. May 18, 2014 #9
    Thanx Curious, exactly the type of thing I was looking for, thanx a million...I kept repeating "unique" in all my Google searches, so there you go...a little variety is always good...

  11. May 18, 2014 #10


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    Note that not all those entries are unique, and some of them just reflect our limited knowledge. And some are... pointless.

    "151 is a palindromic prime." - true, but there are 7 smaller palindromic primes and probably infinitely more larger ones.
    "146 = 222 in base 8." - so what?
  12. May 19, 2014 #11
    Thanx for the clarification mob...funny I would have thought that a compendium of numbers with unique characteristics would be a given in number theory...quite surprised that it's so difficult to find...

  13. May 21, 2014 #12
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